Which of the following numbers is a multiple of 7? ${40,62,68,98,120}$
Solution: The multiples of $7$ are $7$ $14$ $21$ $28$ ..... In general, any number that leaves no remainder when divided by $7$ is considered a multiple of $7$ We can start by dividing each of our answer choices by $7$ $40 \div 7 = 5\text{ R }5$ $62 \div 7 = 8\text{ R }6$ $68 \div 7 = 9\text{ R }5$ $98 \div 7 = 14$ $120 \div 7 = 17\text{ R }1$ The only answer choice that leaves no remainder after the division is $98$ $ 14$ $7$ $98$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $98$ $98 = 2\times7\times7 7 = 7$ Therefore the only multiple of $7$ out of our choices is $98$. We can say that $98$ is divisible by $7$.